Airborne satellite communication links are currently being developed for millimeter wave (K-Ka band) frequencies in order to achieve the broad bandwidths for high data rates. The K-Ka band frequencies require a radome wall design that differs radically from the thin laminate skin, low density core, sandwich design that has prevailed since World War II. For example, the thin-skin A-sandwich design for single band, centimeter wavelength airborne radomes has a typical thickness of about 0.3″, an areal weight of about 0.5 pounds per square foot (PSF), and a transmission efficiency of about 95 percent. Designs for multiband, millimeter wavelength radomes require a nominal half-wave solid laminate core with outer, quarter wave matching layers; this achieves acceptable structural and electrical performance, particularly for low profile shapes that incur high incidence angles. The thickness of these designs is about 0.25″, but their areal weight increases to 1.5 to 2.5 PSF and the transmission efficiency decreases to 80 to 60 percent. The basic multi-layer design for millimeter wavelength radomes has three layers; the addition of a fourth interior matching layer increases the minimum transmission efficiency of the multi-layer design from 60 percent to about 75 percent for the worst cases, but does not reduce the weight. The basic 3-layer, B-sandwich has received a U.S. Pat. No. 7,420,523, B1, dated 2 Sep. 2008, and assigned to Radant Technologies, Inc. and a 4-layer design is disclosed in a U.S. patent application Ser. No. 13/135,263 filed by Radant Technologies, Inc. on 30 Jun. 2011 both of which are incorporated herein in their entirety by this reference. The light weight configuration that is described in the following summary for K-Ka band radome designs also has application to Ku-K-Ka band radome designs.